# Nash type inequalities for fractional powers of non-negative self-adjoint operators

Abstract : Assuming that a Nash type inequality is satisfied by a non-negative self-adjoint operator$A$, we prove a Nash type inequality for the fractional powers $A^{\alpha}$ of $A$. Under someassumptions, we give ultracontractivity bounds for the semigroup $(T_{t,{\alpha}})$ generated by $-A^{\alpha}$.
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Journal articles

https://hal.archives-ouvertes.fr/hal-00001228
Contributor : Patrick Maheux <>
Submitted on : Wednesday, March 10, 2004 - 9:16:18 AM
Last modification on : Tuesday, August 13, 2019 - 11:14:10 AM
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### Citation

Alexander Bendikov, Patrick Maheux. Nash type inequalities for fractional powers of non-negative self-adjoint operators. Transaction of the American Mathematical Society., 2007, 359 (7), pp.3085-3097. ⟨10.1090/S0002-9947-07-04020-2⟩. ⟨hal-00001228⟩

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